01 0.02 0.03 0.04 0.05
Time
Magnitude (dB)
FIGURE 3.11 Temporal amplitude variations of Rayleigh fading.
3.3 RICIAN MULTIPATH FADING PHENOMENON
Here there is a dominant stationary signal or path making a significant contribution to the received
signal power such as a line of sight propagation path. Such is the case when the base station (BS) is
visible to the terminal, the small scale variations are now described with the help of the Rician
distribution.
3.3.1 Mathematical Representation
The Rician distribution is given by the following:
(3.20)
where Io(x) is the modified Bessel function of the first kind and zeroth order, is proportional to
the power of the dominant signal.
A question arises as to how dominant or significant does the signal path need to be? The answer
lies in what is commonly called the K factor and is defined below
(3.21)
This factor describes the ratio between the power of the dominant signal and the power (or variance)
of the multipath signal. For example, let us assume there is no dominant signal, in this case A 0 and
and this distribution now takes on the form of Rayleigh. On the other hand, assume there is
no multipath signal, in this case and , here the distribution approaches the form of an
impulse (or Dirac delta function).
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